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Now showing items 1-10 of 14

#### Equivariant motivic integration and proof of the integral identity conjecture for regular functions

(2019-12-02)

We develop Denef-Loeser’s motivic integration to an equivariant version and
use it to prove the full integral identity conjecture for regular functions. In comparison with
Hartmann’s work, the equivariant Grothendieck ...

#### Neron models of intermediate Jacobians associated to moduli spaces

(2019-12-01)

Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ...

#### Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs

(2019-10-31)

We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ...

#### Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents

(2019-10-21)

In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a ...

#### Some classes of homeomorphisms that preserve multiplicity and tangent cones

(2019-05-28)

In this paper we present some applications of A'Campo-Lê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ...

#### Perverse sheaves on semi-abelian varieties -- a survey of properties and applications

(2019-05)

We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms ...

#### Examples of varieties with index one on C1 fields

(2019-04-16)

Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1.

#### On Lipschitz rigidity of complex analytic sets

(2019-02-26)

We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ...

#### A Lê-Greuel type formula for the image Milnor number

(2019-02)

Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to ...

#### On the length of perverse sheaves on hyperplane arrangements

(2019)

Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...